Brendan Rodgers’ men had the lion’s share of possession but failed to convert their dominance into goals and were punished just before half-time.
Christian Benteke was given time to tee up a long-range effort which creeped past Pepe Reina, with Andreas Weimann finishing a sweeping move to double Villa’s lead moments later.
The Birmingham outfit wrapped up three points when Benteke netted his fifth Premier League goal of the season in the 51st minute before Steven Gerrard scored a late consolation.
“I thought we were outstanding,” Lambert told BBC Sport.
“I thought we looked a threat with Christian Benteke and Andreas Weimann and thought we deserved the win.
“We have been on a terrific run and collectively we have been brilliant. Hopefully, we can continue to climb the table.”
Lambert’s side move three points clear of 18th-placed Wigan Atheltic courtesy of their victory at Anfield.
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